Using complex numbers, the process iterated to generate the Mandelbrot set and the Julia sets takes a very simple form: |
z → z2 + c |
where z and c are complex numbers. |
To iterate the process, pick a complex number c and a complex number z0. Then generate the sequence of complex numbers z1, z2, z3, ... by |
z1 = z02 + c |
z2 = z12 + c |
z3 = z22 + c |
and in general |
zn+1 = zn2 + c |
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How this process generates the
Mandelbrot set and Julia sets is the subject of
Julia Sets and
the Mandelbrot Set.
Here we review the mechanics of |
  |
First, we reformulate the process without using complex numbers. |
Next we do an example of the iteration. |
Return to the Mandelbrot set and Julia sets.